Nicolas Fatio de Duillier (also spelled Faccio or Facio; 16 February 1664 – 10 May 1753) was a Genevan mathematician, natural philosopher, astronomer, inventor, and religious campaigner. Born in Basel, Switzerland, Fatio mostly grew up in the then-independent Republic of Geneva, of which he was a citizen, before spending much of his adult life in England and Holland. Fatio is known for his collaboration with Giovanni Domenico Cassini on the correct explanation of the astronomical phenomenon of zodiacal light, for his "push" or "shadow" theory of gravitation, for inventing the integrating factor as a method for solving ordinary differential equations, for his close association with both Christiaan Huygens and Isaac Newton, and for his role in the Leibniz–Newton calculus controversy. He also invented and developed the first method for fabricating jewel bearings for mechanical watches and clocks.
Elected a Fellow of the Royal Society of London at the age of 24, Fatio never achieved the position and reputation that his early achievements and connections had promised. In 1706 he became involved with a millenarian religious sect, known in London as the "French prophets", and the following year he was sentenced to the pillory for sedition over his role in the publication of the prophecies of Élie Marion, the leader of that sect. Fatio travelled with the French prophets as a missionary, going as far as Smyrna before returning to Holland in 1713, and finally settling in England. His extreme religious views harmed his intellectual reputation, but Fatio continued to pursue technological, scientific, and theological researches until his death at the age of 89.
Early life
Family background Nicolas Fatio was born in Basel, Switzerland, in 1664, into a family that originated in Italy and settled in Switzerland following the Protestant Reformation. One of his cousins was the ill-fated Genevan political reformer Pierre Fatio. Nicolas was the seventh of fourteen children (six brothers and eight sisters) of Jean-Baptiste and Cathérine Fatio, née Barbaud. Jean-Baptiste had inherited a significant fortune, derived from his father in law's interests in iron and silver mining, and in 1672 he moved the family to an estate that he had purchased in Duillier, some twenty kilometres from the town of Geneva. Jean-Baptiste, a devout Calvinist, wished Nicolas to become a pastor, whereas Cathérine, a Lutheran, wanted him to find a place in the court of a Protestant German prince. Instead, the young Nicolas pursued a scientific career.
Nicolas's elder brother, Jean Christophe Fatio, was elected a Fellow of the Royal Society on 3 April 1706. He was married in 1709 to Catherine, daughter of Jean Gassand of Forcalquier, in Provence, and died at Geneva on 18 October 1720. Catherine's will was proved at London in March 1752.Registered in P. C. C. 64, Bettesworth Nicolas himself was never married.
Education and patronage
Nicolas Fatio received his elementary schooling at the Collège de Genève, proceeding in 1678 to the Académie de Genève (now the University of Geneva), where he remained until 1680. At the Académie he came under the influence of the rector, Jean-Robert Chouet, a prominent Cartesian. Before he was eighteen, Fatio wrote to the director of the Paris Observatory, the astronomer Giovanni Domenico Cassini, suggesting a new method of determining the distances to the Sun and Moon from the Earth, as well as an explanation of the form of the rings of Saturn. With Chouet's support, Fatio travelled to Paris in the spring of 1682 and was welcomed received by Cassini.
That same year, Cassini presented his findings on the astronomical phenomenon of zodiacal light. Fatio repeated Cassini's observations in Geneva in 1684, and in 1685 he offered an important development of Cassini's theory, which was communicated by Chouet in the March 1685 number of Nouvelles de la république des lettres. Fatio's own Lettre à M. Cassini touchant une lumière extraordinaire qui paroît dans le Ciel depuis quelques années ("Letter to Mr. Cassini concerning the extraordinary light that has appeared in the Heavens for some years") was published in Amsterdam in 1686. There Fatio correctly explained the zodiacal light as sunlight scattered by an interplanetary dust cloud (the "zodiacal cloud") that straddles the ecliptic plane.
Fatio then studied the dilatation and contraction of the eye's pupil. He described the fibres of the anterior uvea and the choroid in a letter to Edme Mariotte, dated 13 April 1684. That same year he published an article in the Journal des sçavans on how to improve the fabrication of lenses for the objectives of telescopes.
Also in 1684, Fatio met the Piedmontese Count Fenil, who, having offended the Duke of Savoy and the King of France, had taken refuge in the house of Fatio's maternal grandfather in Alsace and then at Duillier. Fenil confided to Fatio his plan to stage a raid on the beach at Scheveningen to kidnap the Dutch Prince William of Orange. Fenil showed Fatio a letter from the Marquis de Louvois, the French Secretary of State, approving of the kidnapping, offering the king's pardon as recompense for the successful completion of the operation, and enclosing an order for money. Fatio betrayed Fenil's plot to Gilbert Burnet, whom he then accompanied to Holland in 1686 to warn Prince William.
Career in Holland and England In Holland, Fatio met Christiaan Huygens in 1682–1683, with whom he began to collaborate on mathematical problems concerning the new infinitesimal calculus. Encouraged by Huygens, Fatio compiled a list of corrections to the published works on differentiation by Ehrenfried Walther von Tschirnhaus. The Dutch authorities wished to reward Fatio, whose mathematical abilities Huygens vouched for, with a professorship. While those plans were delayed, Fatio received permission to visit England in the spring of 1687.
Fatio arrived in England in June 1687, carrying with him the conviction that the two greatest living natural philosophers were Robert Boyle, "for the details of his experiments concerning earthly bodies", and Christiaan Huygens "for physics in general, above all in those areas in which it is involved with mathematics." Fatio hoped to procure Boyle's patronage, and in London he soon made the acquaintance of John Wallis, John Locke, Richard Hampden, and his son John Hampden, among other important figures connected with the Whig party.
Fatio worked out new solutions of the "inverse tangent problem" (i.e., the solution of ordinary differential equations) and was introduced to the Royal Society by Henri Justel. He began to attend Society's meetings in June of that year, when he wrote to Huygens relaying rumours about the upcoming publication by the Society of Isaac Newton's Principia Mathematica. In that letter, Fatio mentions that he had been reproached by several fellows of the Society for "being too Cartesian, and made me to understand that, following the meditations of [Newton], all physics had been completely altered." In the winter of 1687 Fatio went to the University of Oxford, where he collaborated with Edward Bernard, the Savilian Professor of Astronomy, in an investigation into the units of measurement used in the ancient world.
Participation in the Royal Society
Aged only 24, Fatio was elected fellow of the Royal Society on 2 May 1688. That year, Fatio gave an account of Huygens's mechanical explanation of gravitation before the Royal Society, in which he tried to connect Huygens' theory with Newton's work on universal gravitation. Fatio's personal prospects seemed to brighten even further as a result of the Glorious Revolution of 1688–9, which marked the ascendancy of the Whigs and culminated with Parliament deposing the Catholic King James II and giving the English throne jointly to James's Protestant daughter Mary and to her husband, the Dutch Prince William of Orange. Fatio also had an opportunity to enhance his intellectual reputation during Huygens' visit to London in the summer of 1689.
Fatio met Newton, probably for the first time, at a meeting of the Royal Society on 12 June 1689. On 10 July, Fatio accompanied Newton, Huygens, and John Hampden to an audience with the new King. That audience was intended to promote Newton's appointment as provost of King's College, Cambridge, an initiative by Hampden that was not successful. Newton and Fatio soon became friends and Newton even suggested that the two share rooms in London while Newton attended the post-Revolutionary session of Parliament, to which he had been elected in the election of 1689 as member for the University of Cambridge.
Collaborations with Huygens and Newton
In 1690, Fatio wrote to Huygens outlining his own understanding of the physical cause of gravity, which would later become known as "Le Sage's theory of gravitation". Soon after that, he read his letter to Huygens before the Royal Society. Fatio's theory, on which he continued to work until his death, is based on minute particles streaming through space and pushing upon gross bodies, an idea that Fatio probably derived in part from his successful explanation of zodiacal light as sunlight scattered by a cloud of fine dust surrounding the Sun.
Fatio compiled a list of errata to Newton's Principia. Among these was a correction to book II, proposition 36, on the efflux of an ideal fluid through a hole at the bottom of a cylindrical vessel, in which Newton's had obtained a result inconsistent with Torricelli's law. Fatio was able to change Newton's mind with the aid of an experiment, and he shared Newton's amended proposition with Huygens.
Fatio then turned down Newton's offer to reside in Cambridge as his assistant, seeking instead academic preferment in the Netherlands. In the spring of 1690 he went to The Hague as tutor to two of John Hampden's nephews. There, he collaborated with Huygens on problems relating to differential equations, gravity, and optics. At this time, Huygens shared with Gottfried Leibniz some of Fatio's work on differential equations. After one of his pupils died, Fatio returned to London in September 1691. He vied unsuccessfully for the Savilian Professorship of Astronomy at Oxford, a post recently vacated by his friend Edward Bernard. That chair, which was also sought by Edmond Halley, finally went to David Gregory, who had Newton's support.
In February 1691, Fatio exchanged several letters with Huygens in which Fatio revealed his invention of the method of the integrating factor to solve certain ordinary differential equation. Huygens, in turn, communicated Fatio's method to Leibniz. Fatio later communicated that method to Newton, who included it in his treatise De quadratura curvarum ("On the quadrature of curves"), published years later as an appendix to the Opticks (1704). There, Newton credited Fatio with the method, which consists of multiplying an equation of the form
by a factor of to give a new equation
.
If the exponents and can be chosen so that , then the solution to the equation can be expressed as
Fatio initially hoped to collaborate with Newton on a new edition of the Principia that would incorporate Fatio's mechanical explanation of gravity. By the end of 1691, Fatio realised that Newton would not proceed with that project, but he still hoped to collaborate with Newton on corrections to the text of the Principia. In a letter to Huygens, Fatio wrote, concerning those corrections, "I may possibly undertake it myself, as I know no one who so well and thoroughly understands a good part of this book as I do."
Role in Newton's quarrel with Leibniz